Input Uncertainty Quantification Research Articles

Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions

Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: The authors acknowledge financial support from the National Natural Science Foundation of China [Grant NSFC 12101149] and the Hong Kong Research Grants Council [Grants GRF 17201520 and GRF 17206821]. Supplemental Material: The e-companion and data files are available at https://doi.org/10.1287/mnsc.2022.00204 .

Code and Data Repository for A Shrinkage Approach to Improve Direct Bootstrap Resampling Under Input Uncertainty

The goal of this software is to demonstrate the shrinkage bootstrap methods for input uncertainty quantification proposed in "A Shrinkage Approach to Improve Direct Bootstrap Resampling under Input Uncertainty" by Eunhye Song, Henry Lam, and Russell Barton accepted for publication at INFORMS Journal on Computing.

Subsampling to Enhance Efficiency in Input Uncertainty Quantification

Quantifying the impact of input estimation errors in data-driven stochastic simulation often encounters substantial computational challenges due to the entanglement of Monte Carlo and input data noises. In this paper, we propose a subsampling framework to bypass this computational bottleneck, by leveraging the form of the output variance and its estimation error in terms of data size and sampling effort. Compared with standard subsampling in the literature, our motivation is distinctly to reduce the sampling complexity of the two-layer bootstrap required in simulation uncertainty quantification. Compared with standard bootstraps, our subsampling approach provably and experimentally leads to more accurate variance and confidence interval estimations under the same amount of simulation budget.

SAPIUM: A Generic Framework for a Practical and Transparent Quantification of Thermal-Hydraulic Code Model Input Uncertainty

Uncertainty analysis is a key element in nuclear power plant deterministic safety analysis using best-estimate thermal-hydraulic codes and best-estimate-plus-uncertainty methodologies. If forward uncertainty propagation methods have now become mature for industrial applications, the input uncertainty quantification (IUQ) on the physical models still requires further investigations. The Organisation for Economic Co-operation and Development/Nuclear Energy Agency PREMIUM project attempted to benchmark the available IUQ methods, but observed a strong user effect due to the lack of best practices guidance. The SAPIUM project has been proposed toward the construction of a clear and shared systematic approach for IUQ. The main outcome of the project is a first “good-practices” document that can be exploited for safety study in order to reach consensus among experts on recommended practices as well as to identify remaining open issues for further developments. This paper describes the systematic approach that consists of five elements in a step-by-step approach to perform a meaningful model IUQ and validation as well as some good-practice guideline recommendations for each step.

Development of good practice guidance for quantification of thermal-hydraulic code model input uncertainty

Taking into account uncertainties is a key issue in nuclear power plant safety analysis using best estimate plus uncertainty methodologies. It involves two main types of treatment depending on the variables of interest: input parameters or system response quantity. The OECD/NEA PREMIUM project devoted to the first type of variables has shown that inverse methods for input uncertainty quantification can exhibit strong user-effect. One of the main reasons was the lack of a clear guidance to perform a reliable analysis. This work is precisely devoted to the development of a first good practice guidance document for quantification of thermal-hydraulic code model input uncertainty. The developments have been done in the framework of the OECD/NEA SAPIUM project (January 2017–September 2019). This paper provides a summary of the main project outcome. Recommendations and open issues for future developments are also given.

Development of a Pragmatic Approach to Model Input Uncertainty Quantification for BEPU Applications

In the framework of the Organisation for Economic Co-operation and Development/Nuclear Energy Agency PREMIUM [Post-BEMUSE (Best-Estimate Methods Uncertainty and Sensitivity Evaluation) REflood Model Input Uncertainty Methods] benchmark (2012–2015), Tractebel has contributed to the development and the proof-of-concept application of a sampling-based inverse uncertainty quantification (IUQ) approach with the DAKOTA statistical uncertainty and sensitivity analysis tool. This IUQ approach has been applied to quantify the RELAP5/MOD3.3 reflood-related model input uncertainties, based on selected reflood tests [FEBA (Flooding Experiments with Blocked Arrays) and PERICLES]. This paper presents the Tractebel IUQ approach as well as the results of applications to the PREMIUM benchmark. Lessons learned and perspectives for future development are also discussed.

Model uncertainty analysis using data analytics for life-cycle assessment (LCA) applications

Objective uncertainty quantification (UQ) of a product life-cycle assessment (LCA) is a critical step for decision-making. Environmental impacts can be measured directly or by using models. Underlying mathematical functions describe a model that approximate the environmental impacts during various LCA stages. In this study, three possible uncertainty sources of a mathematical model, i.e., input variability, model parameter (differentiate from input in this study), and model-form uncertainties, were investigated. A simple and easy to implement method is proposed to quantify each source. Various data analytics methods were used to conduct a thorough model uncertainty analysis; (1) Interval analysis was used for input uncertainty quantification. A direct sampling using Monte Carlo (MC) simulation was used for interval analysis, and results were compared to that of indirect nonlinear optimization as an alternative approach. A machine learning surrogate model was developed to perform direct MC sampling as well as indirect nonlinear optimization. (2) A Bayesian inference was adopted to quantify parameter uncertainty. (3) A recently introduced model correction method based on orthogonal polynomial basis functions was used to evaluate the model-form uncertainty. The methods are applied to a pavement LCA to propagate uncertainties throughout an energy and global warming potential (GWP) estimation model; a case of a pavement section in Chicago metropolitan area was used. Results indicate that each uncertainty source contributes to the overall energy and GWP output of the LCA. Input uncertainty was shown to have significant impact on overall GWP output; for the example case study, GWP interval was around 50%. Parameter uncertainty results showed that an assumption of ± 10% uniform variation in the model parameter priors resulted in 28% variation in the GWP output. Model-form uncertainty had the lowest impact (less than 10% variation in the GWP). This is because the original energy model is relatively accurate in estimating the energy. However, sensitivity of the model-form uncertainty showed that even up to 180% variation in the results can be achieved due to lower original model accuracies. Investigating each uncertainty source of the model indicated the importance of the accurate characterization, propagation, and quantification of uncertainty. The outcome of this study proposed independent and relatively easy to implement methods that provide robust grounds for objective model uncertainty analysis for LCA applications. Assumptions on inputs, parameter distributions, and model form need to be justified. Input uncertainty plays a key role in overall pavement LCA output. The proposed model correction method as well as interval analysis were relatively easy to implement. Research is still needed to develop a more generic and simplified MCMC simulation procedure that is fast to implement.

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

ABSTRACTArtificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.

Genetic programming based monthly groundwater level forecast models with uncertainty quantification

Modeling hydrogeologic processes facilitates in accurate prediction/forecasting of groundwater level variations. Still, the uncertainty in model prediction is a major concern that requires detailed investigation. There could be several factors which introduce uncertainty such as inherent assumption, various levels of model complexity and simplicity. In general, model inputs, parameters and structure are the major sources of uncertainty while quantifying model prediction uncertainty. In this study, a genetic programming (GP) based models have been employed for forecasting groundwater level variation along with prediction uncertainty quantification. Though various sources induce uncertainty in the model prediction, the input uncertainty quantification has received little attention. Hence, the input uncertainty has been considered for the analysis in this study. The proposed method is demonstrated using measured monthly values of rainfall and corresponding groundwater level data of Amarawathi basin, India. It is observed that the prediction along with uncertainty quantification improves the confidence level of models while making decisions, in particular for effective planning and management of groundwater resources.